This paper presents a new control approach and a dynamic model for engineered flapping flight with many interacting degrees of freedom. This paper explores the applications of neurobiologically inspired control systems in the form of central pattern generators to control flapping-flight dynamics. A rigorous mathematical and control theoretic framework to design complex three-dimensional wing motions is presented based on phase synchronization of nonlinear oscillators. In particular, we show that flapping-flying dynamics without a tail or traditional aerodynamic control surfaces can be effectively controlled by a reduced set of central pattern generator parameters that generate phase-synchronized or symmetry-breaking oscillatory motions of two main wings. Furthermore, by using Hopf bifurcation, we show that tailless aircraft alternating between flapping and gliding can be effectively stabilized by smooth wing motions driven by the central pattern generator network. Results of numerical simulation with a full six-degree-of-freedom flight dynamic model validate the effectiveness of the proposed neurobiologically inspired control approach.